ヽ■′
Materials Transactions, JIM, Vol. 40, No. 8 (1999), pp. 825 to 829
Special Issue on Towards ZnnovatL'on in SuperplastT'city
Simple Evaluation of Superplasticity Using a Tensile Test
wi仙R-type Specimens
Mitsuji Hirohashi, Yun Lu and Masanori Nishizawa†
Department of Electronics and Mechanical Engineering, Chiba University, Chiba 26318522, Japan
Superplastic elongation depends heavily on a value of strain-rate sensitivityindex m. The value of m is obtained by
variOus methods, using specimens of various shapes for uniaxial tensile tests. A specialtechmique is required to measure
the m-value・ In this study, R-type specimens having no smoothed region were employed instead of ordinary smoothed
specimens. A series of tests for variousaluminum alloy sheetsand titanium alloy bars were carried out at elevated
temperatures to evaluate superplasticity. It was di銃cult to measure the m-value using a single R-type specimen.
However, the obtained value uslng more thanthree specimens was in fairly good agreement with the value of smoothed
specimen・ Furthermore, the totalelongation of the gauge length of 6 mm at the bottom of the RIPart could replace that
of the smoothed test-pieces. The obtained value was less scatteredinComparisonwith the value of the smoothed
specimens. Consequently, R-type specimen can be useful for simple evaluation of superplasticity.
(Received February 24, 1999; ln FhalFon June 14, 1999)
Keywords: supeT'Plasticity, tensile test, aluminum alloy, strain rate sensitivity, R-type specimen, total elonga-
lion
I. Introduction
Superplastic behavior is associated with a large
amount of neck-free elongation. Generally, the total
elongation is correlated positively with the strain rate
sensitivityindex of m. Specialtechniques and many test
pleCeSーaLre required to measure the m-Value(1)(2)・ Further-
more, a specialized long furnace should be prepared for
tensile tests of the superplastic materials. The tempera-
ture of the atmosphere in the furnace should be kept at a
constant value for a long time over the elongated speci-
men d也g deformation. The constant strain rate is hard
for the conventional smoothed specimens to handle be-
cause of its large elongation.
} By contrast, the R-type specimen was developed to
ev血ate the superplastic characteristics(1). The ex-
perinentalmethod using the R-type specimen is useful to
deternine the m-Value, theflOw stress and the total
elongation to fracture. These values agree with the results
obt血ed by usmg conventional smoothed specimens.
hl this report, different materials, such as two kinds of
al血umalloys, a zinc alloy and a titanium alloy, are
considered. Furthermore, different shapes of sheet and
bar for tensile specimens are prepared to clarify the su-
perplastic characteristic of the various materials. The
method to obtain the m-value is developed and simplified
using R-type specimens. The freshly induced constitutive
equation for superplasticity is examined for practical
application.
千 Graduate Student, Cbiba University・
II. Experimental Details
1. Materials and specimens
Commercial alloys in the shape of either sheets or bars
were received as shown in Table 1. In this table, Zn1
220/oAl (SPZ) alloy shows remarkable diffusional neck-
ing by comparison with the other alloys. The 良-type
specimens without smoothed reglOnS Were prepared to
evaluate the superplastic characteristics of both the
sheets and bars as shown in Figs. 1(a)-(d). The radius R
of the R-part was constant of 25 mm. A good correla-
tion(1) between the results uslng the ordinary smoothed
specimen and the 良-type specimens for A7475 aluminum
alloy was reported at the condition of R-25 mm. Gauge
marks 3 mm in length as shown in Fig. 1(a) were scribed
in the 良-part of the 良-type specimen.
2. Experimental procedure
The tensile tests uslng an instron type machine were
carried out in air for two kinds aluminum alloys of
A7475 and A5083, and a zinc alloy of SPZ at 803, 803
and 523 Ⅹ, respectively. A titanium alloy of Ti-6Aト4V
was tested in argon at 1173 K. The testing temperature
was kept over the elongated sample usmg three divided
Nichrome wire heaters during deformation. Each speci一
men was suspended by the grlpper in the heated furnace.
An attempt was made to estimate the load on the speci-
men resulting from thermal expansion was balanced ap-
proximately with this hanglng method before the pulling
test was carried out.
826 M. Hirohashi, Y. Luand M・ Nishizawa
Table 1 Chemical composition or the alloys・
Alloymarks Zn Cu Si Fe Mg Mn Cr Ti Al
A7475 5.74 I.50 0.04 0・07 2・57 1 0120
A5083 - - 0.03 0.04 4・70 0・65 0・10
spz 77.9 0.05 - - 0.01 - -
Til6Al14V (6.38 - 6.51)Al-(4.07 - 4・21)V-(0・ 15 - 0・18)Fe-Ti
(a) R-type specimen (sheet)
t
L 唯�
SPZ ��"�1
A5083 ����1.6
(b) smoothed specimen (sheet)
(C) R-type specimen (bar)
for Ti16A1-4V and SPZ
(d) smoothed specimen (bar)
for Ti16A1-4V
Fig. I Shape and dimensions of the R-typeand smoothed specimens
for the tensile test.
IⅡ. Results atLd Discussion
1. Strain rate sensitivity index m
The values of stress are diqerent according to the loI
cation of the R-part in the 良-type specimen・ Of course,
the maximum stress is given in the bottom of the R-part
where strain is concentrated. Therefore, the change in the
stress corresponding to the cross-sectional area of the
R-part follows the strain rate・ The strain rate sensitivity
index m is obtained by assuming that each crossISeCtion
is supported as a uniaxial stress q against the strain rate
台in the whole R-part.
FigtLre 2 shows the relationship between both the
above described values obtained from the R-type speci-
I 0-5 10-4
T,ue St,aim Rate,き/S-1
Fig. 2 Relationship between the true stress assuming uniaxialtensile
stress at each slab of the R-part and the strain rate obtained from the
R-type specimens.
机ens. Generally, plural smoothed specimens were ten-
siled at the different pulling speeds to obtain the m-value・
The procedure uslng a Slngle 良-type specimen was as
follows: the specimen was pulled up to 6 mm, the cross-
head was stopped, the specimen was un fastened, and
then each gauge mark shown in Fig・ 1(a) was carefully
measured by a measurement machine・ The stress, as-
suming uniaxial tension, and the strain rate were calcu-
lated by measurlng each strain・ As the plotted data were
widely scattered, it was dincult to obtain the m-value of
thealloy. It was also technically dincult to measure the
strain of each small slab. Fllrthermore, the condition of
uniaxial tension ceases to be reliable in the reg10n at a
distance from the bottom of the R-part.
Figure 3(b) shows the relation between the nominal
stress instead of the true stress and the pulling speed for
the 良-type specimen・ The stress was calculated by as-
sumlng the stress was uniaxial・ The plot of a nominal
stress on the verticalaxis was calculated simply from the
original cross-sectionalarea, and the horizontal axis was
simply showed the pumng speed or the cross-head speed・
The obtained m-Value of 0.59 wasalmost the same as
the va血e obtained by uslng the conventional smoothed
specimen. Therefore, the gradient of the line in Fig・ 3(a)
was transfered in parallel to theline shown in Fig・ 3(b)・
2. Effects of materials atLd specitnetL Shape on the
m-vane
lt was found that the m-value of thealloy could be
decided easily even if R-type speclmens were used instead
of the smoothed specimens・ Then the various aluminum
alloysand the titaniumalloy were tested to obtain their
m_values. The results for the three kinds of alloys were
shown in Figs・ 4, 5 and 6・ The stresses at the bottom in
the R-part obtained by the 良-type specimens were shown
in order to decide the m-Value more easily. The values of
each alloy were distributed as a straight line, and the m-value was obtained easily as the slope of the line de丘ned
\ヽ_ ヽ-
'a al d
B B B
o・。2竺
OIt!dMJP'SSaJtS9nJト
Simple Evaluation of Superplasticity Using a Tensile Test with R-type Specimens
10~4 1 0-3
True Strain Rate, i /S~1
(a) smoothed specimen
10~1 100 101
. -1
pulling Speed, ; /mm ・ mln
P) R-type specimen
Fig. 3 Comparison of the m-Value with the results for the ordinary
smoothed specimen.
by in these figures.Although the horizontal axes in these
Agures for R-type specimen were simply shown as pulling
speed, the values obtained by boththe R-type and the
smoothed specimens were in approximate agreement.
These m-values were summarized in Table 2. It is
worthy note that the agreement is obtained despite the
differences in shape between sheets and bars.
3. Constitutive equation between stress and strain-
rate
As it well known, the constitutive equation(3) of su-
perplastic materials is
q-K台m (1)
where α is the true stress of the material corresponding to
the strain rateと, m is the strain rate sensitivity indexand
Kis the strength coe缶cient. The value ofKis in eqect the
flow stress at the strain rate of I s-I practically. It was
inpracticalto apply the K-value of the strength coe瓜cient
to the plastic working, because the strain rate showing
the superplasticity of commercial alloys, apart from the
10-3
True Strain Rate, i /S-I
(a)smoothed
827
100● . -1
Pulling Speed, C /mm ・ mln
(b) R-type
Fig. 4 Comparison of the m-values with the results of the smoothed
specimens in A5083 aluminum alloy sheets.
special materials(4)(5) showing superplasticity at a high
strain rate, was different from the strain rate of 1 s-I.
In this paper, the new modified equation proposal to
glVe a more accurate expression is
q-Ksp(訂or Ksp-q(Cfjm (2,
where Ksp is the flow stress at the strain rate of台sp
showing superplasticity of the material. The strain rate of
esp IS expressed in round terms to digit decimalnumbers,
such as a 10-3S-I. The analytical data for the various
specimens werelisted with the other data in Table 2. The
value of Ksp is usefully expressed as the flow stress
showing superplasticity of the material. The difference of
the Ksp-Value obtained uslng the different shapes of
specimen (sheets and bars) became very small in com-
parison with the K-Value. The K-Value changes remarka-
bly in accordance with the change of J乃-Value, because
the value is obtained from the intersection of the exten-
sion of the slope and the strain rate of 1 s~1.
ハUO1
dd∑\j?.SSaとStt!u!uON
tZdMJL)'SSaJTSanJL
828 M. Ilirohashi, Y. Luand M. Nishizawa
■■l■l 綿�"�
SPZ ��
△
△ 盲モ��3��
.I.‥l 呈ツ粐粐�
10-3 10-2
T,ue Strain Rate, i/S~l
(a) smoothed (sheet)
l■l 白�
SPZ ��
m=0.36
.I....l 停貭粳?「�
100 ‥1 101
pulling Speed, ; /mm ・ mln
P) R-type (sheet)
ll 敦ネ��ト����
SPZ ��・■■■■■
・■-
m=0.39
I 鳴��?「貭�
10-1 100 101
. -1
puuing Speed, ;/mm ・ mln
(C) 良-type (bar)
Fig. 5 The m-Value obtained by two shapes of specimen for SPZ zinc
alloys.
4. Total elotLgation to fracture
Formability of superplastic materials depends on the
m-value(3),and the totalelongation in tensile tests is im-
portant, because the elongation depends on the m-value・
On the other hand, it is difRcult to obtain the value of
total elongation llSlng a COnVentional smoothed specimen
having a uniform cross sectioninarea, because of its
huge ductility. And the values are generally dispersed
depending on the breaking part of the specimen.
So a new 氏-type specimen has been proposed to ob-
tained the superplastic characteristics(2). In the results,
101 0-4 1 0-3
True Strain Rate, I /S-1
(a) smoothed (bar)
10110-1 100
. -1
pulling Speed, ; /mm ・ mln
O)) R-type (bar)
Fig. 6 Comparison of the m-Values for the ordinary smoothed and
the R-type specimens in the titaniumalloy.
Table 2 Superplastic characteristic obtained by tensile tests on vari-
ous specimens.
Specimen m-Value KIValue Ks,/MPa
A7475 R-type O・59 1 57 2・7
(sheet) sm.othed 0.58 168 3. I
A5083 R-type O・ 54 206 5 ・08
(sheet) sm。。thed 0. 5 5 225 4. 92
R-type 0.36 47.9 3.99
smootlled 0.39 52. 1 3.59
bar R-type 0.39 58. 3 3.94
R-type 0.37 41 8 32.4
smoothed 0. 42 798 43. 9
m-Value, the flow stress at the strain rate ofとsp and the
constitutive equation of these parameters were ob-
tained easily uslng 良-type specimen. In general, the
tZdMJL)'SSaJ1S9ruL
0ll
tZdMJb nSSaJtSt昌!uJON
HHO1
ddWD'SS9JIStTZtt!uON
t!dMJL)'SSaJtSaruLL
tZd言\D'SS917Slt!u!uON
simple Evaluation of Superplasticity Using a Tensile Testwith R-type Specimens
I.Al川Il. 免ト売��
● ��
A7475 ��ツ�
●∂6:R-type ��
△∂12:Smoothed ��
..tlHHl. 呈ノ?ゥ?「�
10-1 10(1 10l
.一1
pullingspeed, ;・/mm ・ mln
(a) A7475 aluminum alloy sheets
■■■●HHl 白�■l
△全会 ��●
A5083 仞��
+66:R-type ��
.△.6.i:.sP.o禦ed 免ツ�.l
101l■
Pullingspeed, C /mm ・ min
(b) A5083 aluminum alloy sheets
10-1 100 10l● . -1
Pulling speed, C/mm ● mln
(C) sheets and bars of SPZ
Fig. 7 Comparison of the total elongation of R-type specimens with
one of tile Smoothed specimens for various alloys.
fracture in R-type specimenalways occurs near the bot-
tom of the minimum cross sectional area in the RIPart.
Figures 7(a)-(C) shows the elongation of the various
materialSand the different shape of specimen against the
pulling speed. The elongation ∂6 is the total elongation in
829
6 mm gauge length of the bottom of the R-type speci-
men. And the elongation ∂12 is the total elongation
obtained by the ordinary smoothed specimen with a
uniform gauge length of 12 mm. Although the plotted
data were scattered over a narrow range, the value of 66
obtained by R-type specimen was approximately equlVal
lent to the ∂12 Obtained by the smoothed specimen. Espe-
cially, the agreement was shown in Fig. 7(C) whether the
shape of specimen was a sheet or a bar in zinc alloy of
SPZ. The alloy of SPZ shows remarkable dimISional
necking in comparison with the other materials.
Consequently, the 良-type specimen was useful to
evaluate superplasticity in the same manner as using a
smootIled specimen, because the experimental method
was very easy and simple with good reproductive pos-
sibilities.
IV. ConclusioTLS
The R-type specimens in tensile tests both sheets and
bars were useful to evaluate superplastic behaviorin
comparison with ordinary smoothed specimens.
(1) The m-Value can be obtained easily from the log-
log graph paper between the nominal stress in the bottom
of R-partand the pulling speed of the R-type specimens.
(2) The modified constitutional equation is proposed
aS
q-Ksp(訂or Ksp-相m
where esp IS a Strain rate showing the superplasticity of
thealloy, and Ksp is theflOw stress at台sp, respectively.
(3) The total elongation of the 6 mm gauge length in
the bottom of the R-part agrees with the results ob-
tained from the smoothed gauge length for the conven-
tional smoothed specimens.
A ckn o wledgemen ts
The work was supported in p∬t by a Grant-in-Aid for
Scienti丘C Research from the Ministry of Education,
Science, Sports and Culture of Japan, and in part by
Osaka New Materials Center. The authors wish to
acknowledge for the helpful suggestions of Prof.
Y. Takayama of Utsunomiya University in Japan.
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